1.

The line segment joining A(−2, 9) and B(6, 3) is a diameter of a circle with centre C. Find the co-ordinates of C.

Answer»

Given that C is centre of the circle and AB is a diameter of the circle where 

coordinates of A and B are (–2, 9) and (6, 3) respectively. 

∴ C is midpoint of points A and B. 

(∵ Centre is always mid-point of diameter in a circle)

∴ the coordinates of centre C is \((\frac{-2+6}2,\frac{9+3}2)\) = \((\frac{4}2,\frac{12}2)\) = (2,6)

Hence, the co-ordinates of the centre of the circle is (2, 6).



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